In a small bowl, combine melted butter, garlic, lemon juice, and paprika.
Brush the lobster tails with the garlic butter mixture.
Place the lobster tails on the grill, shell side down. Grill for about 10-12 minutes, basting occasionally with the garlic butter mixture, until the meat is opaque and cooked through.
Remove from the grill and serve immediately with additional garlic butter on the side.